This patent document includes a computer program listing appendix that was submitted on a compact disc containing the following files: NPBS1, created Aug. 14, 2002, having an on-disk size of 16.0 kbits; NPBS2, created Aug. 14, 2002, having an on-disk size of 16.0 kbits; NPBS3, created Aug. 14, 2002, having an on-disk size of 16.0 kbits; NPBS4, created Aug. 14, 2002, having an on-disk size of 16.0 kbits; NPBS5, created Aug. 14, 2002, having an on-disk size of 16.0 kbits; NPBS6, created Aug. 14, 2002, having an on-disk size of 16.0 kbits; and NPBS7, created Aug. 14, 2002, having an on-disk size of 16.0 kbits. The material on the compact disc is hereby incorporated by reference herein in its entirety.
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Conventional non-polarizing beamsplitters that are constructed from reflective thin film coatings split an incident beam into a reflected beam and a transmitted beam that have the same polarization as the incident beam. Constructing a non-polarizing beamsplitter can be complicated because for most non-absorbing thin films, the reflectance for the P-polarized beam component (i.e., the component having an electric field in a plane defined by the incident and reflected beams) differs from the reflectance for the S-polarized beam component (i.e., the component having an electric field perpendicular to the plane defined by the incident and reflected beams). The difficulty of constructing a non-polarizing beamsplitter increases in an immersed system where thin film coatings are sandwiched between optical elements.
FIG. 1A illustrates an immersed non-polarizing beamsplitter 100. Beamsplitter 100 includes a beamsplitter coating 120 between optical elements 110 and 130. Optical elements 110 and 130 can be prisms, plates, or other elements made of a material such as an optical quality glass. FIG. 1A specifically shows a configuration where optical elements 110 and 130 are right angle prisms, and an incident monochromatic beam 140 is along a path perpendicular to an input surface of optical element 110 and at an angle of 45xc2x0 with beamsplitter coating 120. As a result, a reflected beam 150 exits perpendicular to an output face of optical element 110, and a transmitted beam 160 exists perpendicular to an output face of optical element 130.
To make beamsplitter 100 non-polarizing, beamsplitter coating 120 is such that for the selected wavelength, S-polarized light and P-polarized light in beam 140 have the same reflectance from beamsplitter coating 120 and the same transmittance through beamsplitter coating 120. FIG. 1B shows the structure of beamsplitter coating 120, which includes 4Q thin films 120-1 to 120-4Q formed of materials having different refractive indices. The choices of materials and thicknesses of thin films 120-1 to 120-4Q provide beamsplitter 100 with the desired reflectance and transmittance of incident beam 140. Incident beam 140, which arrives through optical element 110, partially reflects at the interface between optical element 110 and thin film 120-1, each interface between adjacent pairs of thin filns [120-1, 120-2] to [120-(Nxe2x88x921),120-4Q], and the interface between thin 120-4Q and optical element 130. The partial reflections combine and interfere to form reflected beam 150, while the portion of incident beam 140 not reflected (and not absorbed) becomes a transmitted beam 160.
Equations 1 are formulas for the reflection coefficients rs and rp respectively for S-polarized and P-polarized light in beamsplitter 100 when each of thin films 120-1 to 120-N has an optical thickness that is one quarter of the wavelength of incident beam 140. In Equations 1, values N0, N1 to N4Q, and N4Q+1 are the respective refractive indices of element 110, thin films 120-1 to 120-4Q, and element 130; and values xcex80, xcex81 to xcex84Q, and xcex84Q+1 are the respective propagation angles of the transmitted beams in element 110, thin films 120-1 to 120-4Q, and element 130.
Equations 1:                     rs        =                  xe2x80x83                ⁢                              1            -                          U              *              W                                            1            +                          U              *              W                                                              rp        =                  xe2x80x83                ⁢                              1            -                          U              /              W                                            1            +                          U              /              W                                                              U        =                  xe2x80x83                ⁢                                            N              0                        *                          N              2                        *                          N              4                        *            …            ⁢                          xe2x80x83                        ⁢                          N                              4                ⁢                Q                                                                        N              1                        *                          N              3                        *            …            ⁢                          xe2x80x83                        ⁢                          N                                                4                  ⁢                  Q                                -                1                                      *                          N                                                4                  ⁢                  Q                                +                1                                                                            W        =                  xe2x80x83                ⁢                              cos            ⁢                          xe2x80x83                        ⁢                          θ              0                        *            cos            ⁢                          xe2x80x83                        ⁢                          θ              2                        *            …            ⁢                          xe2x80x83                        ⁢            cos            ⁢                          xe2x80x83                        ⁢                          θ                              4                ⁢                Q                                                          cos            ⁢                          xe2x80x83                        ⁢                          θ              1                        *            cos            ⁢                          xe2x80x83                        ⁢                          θ              3                        *            …            ⁢                          xe2x80x83                        ⁢            cos            ⁢                          xe2x80x83                        ⁢                          θ                                                4                  ⁢                  Q                                +                1                                                        
A non-polarizing bearnsplitter is equally efficient at reflecting S-polarized and P-polarized light. The reflection coefficient rs of non-polarizing beamsplitter 100 thus must be non-zero and equal in magnitude to the reflection coefficient rp of the non-polarizing beamsplitter 100. FIG. 1B illustrates a combination of thin films 120-1 to 120-4Q for which reflection coefficients rs and rp are non-zero and equal because one of factor W or U of Equations 1 is equal to 1 and the other factor U or W is not equal to 1. Non-polarizing beamsplitter 100 uses three materials H, M, and L for thin film layers 120-1 to 120-4Q and organizes thin film layers 120-1 to 120-4Q into Q groups of four layers each. Each group of four thin film layers includes a first layer of material M having an intermediate refractive index NM, a second layer of material H having a higher refractive index NH, a third layer of material M, and a fourth layer of material L having a low refractive index NL. The three materials are selected so that refractive indices NH, NM, and NL make one factor W or U equal to 1.
Factor W of Equations 1 depends on the propagation angles xcex81 to xcex84Q for light passing through thin films 120-1 to 120-4Q, and the propagation angles depend on the refractive indices N0, N1 to N4Q, and N4Q+1. Snell""s Law as applied in Equation 2 indicates that the product of the refractive index and the sine of the propagation angle is a constant L for all of the thin films 120-1 to 120-4Q. Accordingly, any two of thin films 120-1 to 120-4Q that have the same refractive index will have the same propagation angle.
Equation 2
N0*sin xcex80=N1*sin xcex81=N2*sin xcex82 . . . =N4Q+1*sin xcex84Q+1 =L
In beamsplitter 100, thin films having refractive indices NM, NH, and NL respectively have propagation angles xcex8M, xcex8H, and xcex8L. When the elements 110 and 130 have the same refractive index, cosxcex80 is equal to cosxcex84Q+1, and use of propagation angles xcex8M, xcex8H, and xcex8L simplifies the formula for factor W as illustrated in Equation 3. If incident angle xcex80 (e.g., 45xc2x0) and refractive indices NM, NH, and NL make angles xcex8M, xcex8H, and xcex8L satisfy Equation 4, factor W is equal to 1, and beamsplitter 100 is non-polarizing.
Equation 3:   W  =                    cos        ⁢                  xe2x80x83                ⁢                  θ          0                *        cos        ⁢                  xe2x80x83                ⁢                  θ          2                *        …        ⁢                  xe2x80x83                ⁢        cos        ⁢                  xe2x80x83                ⁢                  θ                      4            ⁢            Q                                      cos        ⁢                  xe2x80x83                ⁢                  θ          1                *        cos        ⁢                  xe2x80x83                ⁢                  θ          3                *        …        ⁢                  xe2x80x83                ⁢        cos        ⁢                  xe2x80x83                ⁢                  θ                                    4              ⁢              Q                        +            1                                =                  (                              cos            ⁢                          xe2x80x83                        ⁢                          θ              H                        *            cos            ⁢                          xe2x80x83                        ⁢                          θ              L                                            cos            ⁢                          xe2x80x83                        ⁢                          θ              M                        *            cos            ⁢                          xe2x80x83                        ⁢                          θ              M                                      )            Q      
Equation 4:             cos      ⁢              xe2x80x83            ⁢              θ        H            *      cos      ⁢              xe2x80x83            ⁢              θ        L                    cos      ⁢              xe2x80x83            ⁢              θ        M            *      cos      ⁢              xe2x80x83            ⁢              θ        M              =  1
The materials suitable for optical-quality thin films 120 limit the available refractive indices. An exemplary solution for Equation 4 can be approximately achieved in non-polarizing beamsplitter 100 for light having a wavelength of about 633 nm and an incident angle xcex80 of 45xc2x0 by using aluminum oxide (AL2O3), titanium oxide (TiO2), and magnesium fluoride (MgF2) as materials H, M, and L, respectively. Titanium oxide (TiO2) has a refractive index NH of about 2.27. Aluminum oxide (AL2O3) has a refractive index NM of about 1.62, and magnesium fluoride (MgF2) with a refractive index NL of about 1.37. The intensity of reflected beam 150 for this solution depends on the number Q of groups of thin films. For Q equal to 5, the reflected power ratio Rs for S-polarized light is about 48.1%, and the reflected power ratio Rp for P-polarized light is about 52.6%, which are suitable for many applications of a 50% non-polarizing beamsplitter.
With the above structure, immersed non-polarizing beamsplitter 100 has a large number (e.g., 10) of thin films made of AL2O3. Thin films of AL2O3 can absorb water vapor from their surroundings, which results in mottling. This mottling can unpredictably change the phase profile of reflected and transmitted beams 150 and 160, and the accumulation of the phase profile changes from a larger number of thin film layers of AL2O3 can reach intolerable levels for precision optical systems such as interferometers. Non-polarizing beamsplitters having few or no thin film layers of AL2O3 and methods for designing non-polarizing beamsplitters having few or no thin film layers of problematic materials are thus sought.
In accordance with an aspect of the invention, a non-polarizing beamsplitter contains multiple groups of thin film layers and one or more additional thin film layers. The thin film groups do not by themselves provide non-polarizing reflections, but the additional thin films compensate so that reflections and transmissions are non-polarizing. The additional thin film layers provide additional design freedom and the flexibility necessary to avoid the repeated layers of problematic materials such as AL2O3.
One specific embodiment of the invention is an immersed non-polarizing beamsplitter. The beamsplitter includes multiple thin film groups and one or more additional thin films. Each thin film group typically consists of a layer of a first material having a higher refractive index, two layers of a second material having an intermediate refractive index, and a layer of a third material having a lower refractive index. At least one of the additional thin films contains a fourth material that differs from the first, second, and third materials. Each of the additional thin films and the layers in the thin film groups has an optical thickness equal to one quarter of a wavelength of an incident light beam being split.
The additional thin film layers can precede, be between, or follow the thin film groups along a path of a transmitted beam of the beamsplitter. Generally, an even number of additional thin films fill the space between an adjacent pair of the thin film groups, but any number of additional films can precede or follow the thin film groups.
Each thin film group in some exemplary embodiments of the invention consists of: a layer of titanium oxide (TiO2), which is the first material; two layers of yttrium oxide (Y2O3), which is the second material; and a layer of magnesium fluoride (MgF2), which is the third material. The order of the layers in the thin film groups can vary. A first additional thin film layer is a layer of aluminum oxide (Al2O3), which is the fourth material. A second additional thin film layer that is adjacent the first additional thin film layer can be made of the first, second, or third material, (e.g., Y2O3) to minimize the number of different materials required. The first and second additional thin film layers typically fill the space between two of the thin film groups. Using these materials, a non-polarizing beamsplitter coating that reflects about 50% of incident light having a wavelength of about 633 nm consists of six thin film groups, and the first and second additional thin film layers. A non-polarizing beamsplitter coating that reflects about 33% of incident light having a wavelength of about 633 nm consists of an initial thin film layer made of a material such as MgF2, four thin film groups, the first additional thin film layer, and the second additional thin film layer.
Another embodiment of the invention is a design method for a non-polarizing beamsplitter. The method starts with selecting a set of materials to be used in thin film groups. A thin film group using the selected materials can fail to provide a non-polarizing reflection, and can thus be limited to materials having the most desirable properties. To the extent that the thin film groups fail to provide a non-polarizing reflection, a structure consisting of the thin film groups and one or more additional thin films can be selected. In selecting the structure, the number of the thin film groups can be selected according to a desired reflectance of the non-polarizing beamsplitter. The structures available for selection vary in the number and positions of the additional thin films. A calculation based on the selected structure indicates the requirements for a non-polarizing beamsplitter and determines at least one refractive index for at least one additional thin film layer. Materials having the calculated refractive indices are then sought. If no suitable material is identified as having one of the calculated refractive indices, another choice of materials for the thin film groups can be made, or another structure is selected and evaluated. If a suitable material is found, the dependence of the reflectance on wavelength can be evaluated for different ordering of the layers in the thin film groups and positions of the additional thin films relative to the thin film groups. Structures with particular materials and layer orders that provide the desired reflectance with minimal wavelength dependence can be constructed and experimentally evaluated.